"What is the derivative of xy?" was answered by our experts

klupko5HR

Answered question

2022-11-25

What is the derivative of

x y

?

Answer & Explanation

Jadyn Huynh

Beginner2022-11-26Added 7 answers

Rule for derivative products:

\frac{d (u v)}{d x} = u \frac{d v}{d x} + v \frac{d u}{d x}

Differentiate the function

x y

with respect to

x

, we get

\frac{d}{d x} (x y) = x (\frac{d y}{d x}) + y (\frac{d x}{d x})

\Rightarrow

\frac{d}{d x} (x y) = x (\frac{d y}{d x}) + y (1)

\Rightarrow

\frac{d}{d x} (x y) = x (\frac{d y}{d x}) + y

Hence, the derivative of

x y

is

x (\frac{d y}{d x}) + y

.

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